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Algorithm

2010

The FFT is a computationally efficient algorithm for computing a Discrete Fourier Transform (DFT) of sample sizes that are a positive integer power of 2. The DFT X ( k), k = 0, K, N −1of a sequence xn (), n = 0, K, N−1 is defined as

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ALGORITHM?

Multi-proposal Metropolis-hastings, Monte Carlo, Jean-françois Delmas et al. · 2009

Abstract. The waste-recycling Monte Carlo (WR) algorithm introduced by physicists is a modification of the (multi-proposal) Metropolis-Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) Metropolis-Hastings algorithm only uses the accepted proposals. In this paper, we extend the WR algorithm into a general control variate technique and exhibit the optimal choice of the control variate in terms of asymptotic variance. We also give an example which shows that in contradiction to the intuition of physicists, the WR algorithm can have an asymptotic variance larger than the one of the Metropolis-Hastings algorithm. However, in the particular case of the Metropolis-Hastings algorithm called Boltzmann algorithm, we prove that the WR algorithm is asymptotically better than the Metropolis-Hastings algorithm. This last property is also true for the multi-proposal Metropolis-Hastings algorithm. In this last framework, we consider a linear parametric generalization of WR, and we propose an estimator of the explicit optimal parameter using the proposals. 1.

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Algorithm

Ashish Sharma, Rengakrishnan Subramanian · 2001

This paper is concerned with finding a linear-time algorithm for implementing a function pivotbis, which is used in Quick Sort algorithm. The function partitions an array into three parts, elements less than, equal to and greater than an element pivot, which is the first element of the array. The algorithm scans the input array only once and uses no auxiliary arrays.

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Algorithm

Matthias Leese · Repository for Publications and Research Data (ETH Zurich) · 2025

This chapter explores the increasingly prominent role of algorithms in polic ing and criminal justice. Engaging with their inherently non-neutral nature and issues of opaqueness introduced by algorithmic knowledge making, the chapter highlights im plications for accountability and democratic control. It concludes by spelling out some of the challenges for research on algorithms in policing and criminal justice contexts.

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